Search Results (294)

A geodesic or geodetic line on a sphere is called the orthodrome. Research has shown that the orthodrome can be defined in a large number of ways. This article provides an overview of various definitions of the orthodrome. We recall the definitions of the orthodrome according to the greats of geodesy, such as Bessel and Helmert. We derive the equation of the orthodrome in the geographic coordinate system and in the Cartesian spatial coordinate system. A geodesic on a surface is a curve for which the geodetic curvature is zero at every point. Equivalent expressions of this statement are that at every point of this curve, the principal normal vector is collinear with the normal to the surface, i.e., it is a curve whose binormal at every point is perpendicular to the normal to the surface, and that it is a curve whose osculation plane contains the normal to the surface at every point. In this case, the well-known Clairaut equation of the geodesic in geodesy appears naturally. It is found that this equation can be written in several different forms. Although differential equations for geodesics can be found in the literature, they are solved in this article, first, by taking the sphere as a special case of any surface, and then as a special case of a surface of rotation. At the end of this article, we apply calculus of variations to determine the equation of the orthodrome on the sphere, first in the Bessel way, and then by applying the Euler–Lagrange equation. Overall, this paper elaborates a dozen different approaches to orthodrome definitions. Full article

Background and Objective: This study presents a combined osteometric and biomechanical analysis of a Korean female cadaver exhibiting bilateral lower limb bone asymmetry with abnormal curvature and callus formation on the left femoral midshaft. Methods: To investigate bilateral bone length differences, osteometric measurements were conducted at standardized landmarks. Additionally, we developed three gait models using Meta Motivo, an open-source reinforcement learning platform, to analyze how skeletal asymmetry influences stride dynamics and directional control. Results: Detailed measurements revealed that the left lower limb bones were consistently shorter and narrower than their right counterparts. The calculated lower limb lengths showed a bilateral discrepancy ranging from 39 mm to 42 mm—specifically a 6 mm difference in the femur, 33 mm in the tibia, and 36 mm in the fibula. In the gait pattern analysis, the normal model exhibited a straight-line gait without lateral deviation. In contrast, the unbalanced, non-learned model demonstrated compensatory overuse and increased stride length of the left lower limb and a tendency to veer leftward. The unbalanced, learned model showed partial gait normalization, characterized by reduced limb dominance and improved right stride, although directional control remained compromised. Conclusions: This integrative approach highlights the biomechanical consequences of lower limb bone discrepancy and demonstrates the utility of virtual agent-based modeling in elucidating compensatory gait adaptations. Full article

Identifying habitat characteristics is essential for conserving critically endangered species. When quantifying species habitat characteristics, ignoring data types may lead to misunderstandings about species’ specific habitat requirements. This study focused on the critically endangered Chinese pangolin in Guangdong Province, China, and divided the study area into 600 m × 600 m grids based on its average home range. The burrow number within each grid was obtained through line transect surveys, with burrow numbers/line transect lengths used as direct indicators of habitat utilization intensity. The relationships with sixteen environmental variables, which could be divided into three categories, including topographic, human disturbance and land cover composition, were quantified using the GAM method. We also converted continuous data into binary data (0, 1), constructed GAMs and compared them with habitat utilization intensity models. Our results indicate that the habitat utilization intensity model identified profile curvature and slope as primary factors, showing a nonlinear response to profile curvature (Edf = 5.610, p = 0.014) and a positive relationship with slope (Edf = 1.000, p = 0.006). The presence–absence model emphasized distance to water (Edf = 1.000, p = 0.014), slope (Edf = 1.709, p = 0.043) and aspect (Edf = 2.000, p = 0.026). The intensity model explained significantly more deviance, captured complex nonlinear relationships and supported higher model complexity without overfitting. This study demonstrates that habitat utilization intensity data provides a more ecologically informative basis for in situ conservation (e.g., identifying core habitats), and the process from habitat selection to habitat utilization should be integrated to reveal species’ habitat characteristics. Full article

Unbalanced accelerations occurring during tram travel have a significant impact on passenger comfort and safety, as well as on the rate of wear and tear on infrastructure and rolling stock. Ideally, these dynamic forces should be monitored continuously in real-time; however, traditional systems require high-precision accelerometers and proprietary software—investments often beyond the reach of municipally funded tram operators. To this end, as part of the research project “Accelerometer Measurements in Rail Passenger Transport Vehicles”, pilot measurement campaigns were conducted in Poland on tram lines in Gdańsk, Toruń, Bydgoszcz, and Olsztyn. Off-the-shelf smartphones equipped with MEMS accelerometers and GPS modules, running the Physics Toolbox Sensor Suite Pro app, were used. Although the research employs widely known methods, this paper addresses part of the gap in affordable real-time monitoring by demonstrating that, in the future, equipment equipped solely with consumer-grade MEMS accelerometers can deliver sufficiently accurate data in applications where high precision is not critical. This paper presents an analysis of a subset of results from the Gdańsk tram network. Lateral (x) and vertical (z) accelerations were recorded at three fixed points inside two tram models (Pesa 128NG Jazz Duo and Düwag N8C), while longitudinal accelerations were deliberately omitted at this stage due to their strong dependence on driver behavior. Raw data were exported as CSV files, processed and analyzed in R version 4.2.2, and then mapped spatially using ArcGIS cartograms. Vehicle speed was calculated both via the haversine formula—accounting for Earth’s curvature—and via a Cartesian approximation. Over the ~7 km route, both methods yielded virtually identical results, validating the simpler approach for short distances. Acceleration histograms approximated Gaussian distributions, with most values between 0.05 and 0.15 m/s², and extreme values approaching 1 m/s². The results demonstrate that low-cost mobile devices, after future calibration against certified accelerometers, can provide sufficiently rich data for ride-comfort assessment and show promise for cost-effective condition monitoring of both track and rolling stock. Future work will focus on optimizing the app’s data collection pipeline, refining standard-based analysis algorithms, and validating smartphone measurements against benchmark sensors. Full article

This paper primarily investigates the response and failure behavior of 6063-T5 aluminum alloy square tubes with varying outer side lengths under symmetric curvature-controlled cyclic bending in different bending directions. The response is characterized by the moment–curvature relationship and the variation in the outer side length with respect to curvature, whereas failure is characterized by the relationship between the controlled curvature and the number of cycles required to initiate buckling. The outer side lengths studied are 20 mm, 30 mm, 40 mm, and 50 mm, and the bending directions considered are 0°, 22.5°, and 45°. The moment–curvature curves exhibited cyclic hardening, and stable loops were formed for all outer side lengths and bending directions. An increase in the outer side length resulted in a higher peak bending moment, while a greater bending direction led to a slight increase in the peak bending moment. For a fixed bending direction, the curves representing the variation of the outer side length (defined as the change in length divided by the original length) with respect to curvature displayed symmetry, serrated features, and an overall increasing trend as the number of cycles increased, irrespective of the specific outer side length. In addition, increasing either the outer side length or altering the bending direction led to a larger variation in the outer side length. As for the relationship between curvature and the number of cycles required to initiate buckling, the data for each bending direction and each of the four outer side lengths formed distinct straight lines on a double-logarithmic plot. Based on the experimental observations, empirical equations were developed to characterize these relationships. These equations were then used to predict the experimental data and showed excellent agreement with the measured results. Full article

The development of Advanced Driver Assistance Systems (ADASs) has reached a stage where, in addition to the traditional challenges of path planning and control, there is an increasing focus on the behavior of these systems. Assistance functions shall be personalized to deliver a full user experience. Therefore, driver modeling is a key area of research for next-generation ADASs. One of the most common tasks in everyday driving is lane keeping. Drivers are assisted by lane-keeping systems to keep their vehicle in the center of the lane. However, human drivers often deviate from the center line. It has been shown that the driver’s choice to deviate from the center line can be modeled by a linear combination of preview curvature information. This model is called the Linear Driver Model. In this paper, we fit the LDM parameters to real driving data. The drivers are then clustered based on the individual parameters. It is shown that clusters are not only formed by the numerical similarity of the driver parameters, but the drivers in a cluster actually have similar behavior in terms of path selection. Finally, an Extended Kalman Filter (EKF) is proposed to learn the model parameters at run-time. Any new driver can be classified into one of the driver type groups. This information can be used to modify the behavior of the lane-keeping system to mimic human driving, resulting in a more personalized driving experience. Full article

Defects arising from the 3D printing process of continuous fiber-reinforced thermoplastic composites primarily hinder their overall performance. These defects particularly include twisting, folding, and breakage of the fiber bundle, which are induced by printing trajectory errors. This study presents a follow-up theory assumption to address such issues, elucidates the formation mechanism of printing trajectory errors, and examines the impact of key geometric parameters—trace curvature, nozzle diameter, and fiber bundle diameter—on these errors. An error model for printing trajectory is established, accompanied by the proposal of a trajectory error compensation method premised on maximum printable curvature. The presented case study uses CCFRF/PA as an exemplar; here, the printing layer height is 0.1~0.3 mm, the fiber bundle radius is 0.2 mm, and the printing speed is 600 mm/min. The maximum printing curvature, gauged by the printing trajectory of a clothoid, is found to be 0.416 mm⁻¹. Experimental results demonstrate that the error model provides accurate predictions of the printed trajectory error, particularly when the printed trajectory forms an obtuse angle. The average prediction deviations for line profile, deviation kurtosis, and deviation area ratio are 36.029%, 47.238%, and 2.045%, respectively. The error compensation effectively mitigates the defects of fiber bundle folding and twisting, while maintaining the printing trajectory error within minimal range. These results indicate that the proposed method substantially enhances the internal defects of 3D printed components and may potentially be applied to other continuous fiber printing types. Full article

A straightforward and versatile numerical approach is proposed for the nonlinear analysis of single and double-curvature masonry structures. The method is designed to broaden accessibility to both experienced and less specialized users. Masonry units are discretized with elastic quadrilateral elements, while mortar joints are modeled with a combination of elastic orthotropic plate elements or shear panels and elastic perfectly brittle trusses (cutoff bars). This method employs the simplest inelastic finite element available in any commercial software to lump nonlinearities exclusively within the mortar joints. It effectively captures the failure of curved structures under Mode 1 deformation, reproducing the typical collapse mechanism of unreinforced arches and vaults via flexural plastic hinges. The proposed method is benchmarked through three case studies drawn from the literature, each supported by experimental data and numerical results of varying complexity. A comprehensive evaluation of the global force–displacement curves, along with the analysis of the thrust line and the evolution of nonlinearities within the model, demonstrates the effectiveness, reliability, and simplicity of the approach proposed. By bridging the gap between advanced simulation and practical application, the approach provides a robust tool suitable for a wide range of users. This study contributes to a deeper understanding of the behavior of unreinforced curved masonry structures and lays a base for future advancements in the analysis and conservation of historical heritage. Full article

Due to the complexity of the unstructured environment and the high-level requirement of smoothness when a tracked transportation vehicle is traveling, making the vehicle travel as safely and smoothly as when a skilled operator is maneuvering the vehicle is a critical issue worth studying. To this end, this study proposes a trajectory-planning method for human-like maneuvering. First, several field equipment operators are invited to manipulate the model vehicle for obstacle avoidance driving in an outdoor scene with densely distributed obstacles, and the manipulation data are collected. Then, in terms of the lateral displacement, by comparing the similarity between the data as well as the curvature change degree, the data with better smoothness are screened for processing, and a dataset of human manipulation behaviors is established for the training and testing of the trajectory-planning network. Then, using the dynamic parameters as constraints, a two-stage planning approach utilizes a modified deep network model to map trajectory points at multiple future time steps through the relationship between the spatial environment and the time series. Finally, after the experimental test and analysis with multiple methods, the root-mean-square-error and the mean-average-error indexes between the planned trajectory and the actual trajectory, as well as the trajectory-fitting situation, reveal that this study’s method is capable of planning long-step trajectory points in line with human manipulation habits, and the standard deviation of the angular acceleration and the curvature of the planned trajectory show that the trajectory planned using this study’s method has a satisfactory smoothness. Full article

To investigate the erosion and deposition evolution characteristics of the Xinqiman–Kelelik reach along the main stem of the Tarim River, this study analyzed river channel dynamics and planform morphological changes using Landsat satellite imagery (1993–2024) and hydrological data (water discharge and sediment load) from gauge stations. The results show that the thalweg line swings indefinitely in the river. The thalweg length increased by 29 km, while the mean channel width decreased by 0.28 km. The sinuosity index rose from 1.95 to 2.34, indicating a gradual intensification of channel curvature. The north bank is in a state of siltation, while the south bank is in a state of erosion. The riverbank exhibited an overall southward migration. The farmland area in the study area increased from 1510 hectares in 1993 to 5140 hectares in 2024. During this period, the thalweg near the water-diversion sluice continuously shifted toward the sluice side. To ensure flood protection safety for farmlands and villages on both banks, as well as ecological water diversion, river channel regulation and channel pattern control should be implemented. Full article

The automation of adhesive application in footwear manufacturing is challenging due to complex surface geometries and model variability. This study presents an integrated 3D vision-based robotic system for adhesive spraying on lasted uppers. A triangulation-based scanning setup reconstructs each upper into a high-resolution point cloud, enabling customized spraying path planning. A six-axis robotic arm executes the path using an adaptive transformation matrix that aligns with surface normals. UV fluorescent dye and inspection are used to verify adhesive coverage. Experimental results confirm high repeatability and precision, with most deviations within the industry-accepted ±1 mm range. While localized glue-deficient areas were observed around high-curvature regions such as the toe cap, these remain limited and serve as a basis for further system enhancement. The system significantly reduces labor dependency and material waste, as observed through the replacement of four manual operators and the elimination of adhesive over-application in the tested production line. It has been successfully installed and validated on a production line in Hanoi, Vietnam, meeting real-world industrial requirements. This research contributes to advancing intelligent footwear manufacturing by integrating 3D vision, robotic motion control, and automation technologies. Full article

This study proposes the use of Physics-Informed Neural Networks (PINNs) to further advance the curvature interference analysis method. The nonlinear equation system encountered in determining the curvature interference limit line is embedded into the PINN loss function, thereby enabling the solution of high-dimensional, nonlinear equations. Computational results demonstrate that the PINN model achieves a solution accuracy on the order of 10⁻¹³ when solving multidimensional nonlinear systems, which is comparable to the classical Fsolve algorithm. The curvature interference analysis reveals the presence of two curvature interference boundary lines, although they rarely extend to the worm gear tooth surface. A study on the influence of design parameters on the interference boundaries indicates that the axial installation distance has the greatest impact. Inadequate axial spacing causes the interference limit line to shift toward the inner end of the worm gear, significantly increasing the risk of interference in that region. The proposed curvature interference analysis method based on PINNs can be extended to other types of gear drives. It also lays the foundation for future work on establishing both forward and inverse mappings between design parameters and curvature interference using PINNs. Full article

The volume-of-fluid (VOF) method is widely used for multiphase flow simulations, where the VOF function implicitly represents the interface through the volume fraction field. The height function (HF) method on a Cartesian grid integrates the volume fractions of a column of cells across the interface. A stencil of three consecutive heights and centered finite differences compute the unit normal $\mathbf{n}$ and the curvature $\kappa$ with second-order convergence with grid refinement. The interface line can cross more than one cell of the column, and the value of the geometrical properties of the interface should be interpolated in the cut cells. We propose a numerical algorithm to interpolate the geometrical data that removes the inconsistency between theoretical and numerical results presented in many papers. A constant approximation in the column of cells provides first-order convergence with grid refinement, while linear and quadratic interpolations indicate second-order convergence. The numerical results obtained with analytical curves agree with the theoretical development presented in this study. Full article

Micro-terrain recognition plays a crucial role in the planning, design, and safe operation of transmission lines. To achieve intelligent and automatic recognition of micro-terrain surrounding transmission lines, this paper proposes an improved semantic segmentation model based on UNet++. This model expands the single encoder into multiple encoders to accommodate the input of multi-source geographic features and introduces a gated fusion module (GFM) to effectively integrate the data from diverse sources. Additionally, the model incorporates a dual attention network (DA-Net) and a deep supervision strategy to enhance performance and robustness. The multi-source dataset used for the experiment includes the Digital Elevation Model (DEM), Elevation Coefficient of Variation (ECV), and profile curvature. The experimental results of the model comparison indicate that the improved model outperforms common semantic segmentation models in terms of multiple evaluation metrics, with pixel accuracy (PA) and intersection over union (IoU) reaching 92.26% and 85.63%, respectively. Notably, the performance in identifying the saddle and alpine watershed types has been enhanced significantly by the improved model. The ablation experiment results confirm that the introduced modules contribute to enhancing the model’s segmentation performance. Compared to the baseline network, the improved model enhances PA and IoU by 1.75% and 2.96%, respectively. Full article

The evaluation of imagery style in industrial product design is inherently subjective, making it difficult for designers to accurately capture user preferences. This ambiguity often results in suboptimal market positioning and design decisions. Existing methods, primarily limited to single product categories, rely on labor-intensive user surveys and computationally expensive data processing techniques, thus failing to support cross-category collaboration. To address this, we propose an Imagery Style Evaluation (ISE) method that enables rapid, objective, and intelligent assessment of imagery styles across diverse industrial product forms, assisting designers in better capturing user preferences. By combining Kansei Engineering (KE) theory with four key visual morphological features—contour lines, edge transition angles, visual directions and visual curvature—we define six representative style paradigms: Naturalness, Technology, Toughness, Steadiness, Softness, and Dynamism (NTTSSD), enabling quantification of the mapping between product features and user preferences. A deep learning-based ISE architecture was constructed by integrating the NTTSSD paradigms into an enhanced YOLOv5 network with a Convolutional Block Attention Module (CBAM) and semantic feature fusion, enabling effective learning of morphological style features. Experimental results show the method improves mean average precision (mAP) by 1.4% over state-of-the-art baselines across 20 product categories. Validation on 40 product types confirms strong cross-category generalization with a root mean square error (RMSE) of 0.26. Visualization through feature maps and Gradient-weighted Class Activation Mapping (Grad-CAM) further verifies the accuracy and interpretability of the ISE model. This research provides a robust framework for cross-category industrial product style evaluation, enhancing design efficiency and shortening development cycles. Full article